[(x-1)/x-(x-2)/(x-1)]÷[(2x²-x)/(x²+2x+1)]
=[(x-1)²-x(x-2)]/x(x-1)÷[x(2x-1)/(x+1)²]
=[1/x(x-1)]*[(x+1)²/x(2x-1)]
=(x+1)²/x²(x-1)(2x-1)
∵x²=x+1
∴原式=(x+1+2x+1)/(x+1)(x-1)(2x-1)
=(3x+2)/(x²-1)(2x-1)
=(3x+2)/(x+1-1)(2x-1)
=(3x+2)/(2x²-x)
=(3x+2)/(2x+2-x)
=(3x+2)/(x+2)
题目可能有错误,不然只能由x²-x-1=0解出x,再代入求值了。就做到这儿吧。
追问我也做到了这儿,不过谢谢啊
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